The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  1  1  1  1  2  2  2  1  1  1  1  4  4  4  0  0  0  2  2  2  2  2  1  2  2  2  4  0  4  0  4  4  0
 0  4  0  4  0  0  4  4  0  0  4  4  0  0  4  4  0  0  4  0  4  4  4  0  0  4  4  0  4  4  0  0  4  4  0  4  4  4  4  0  0  0  4  4  0  0  0  4  0  4  4  0  0  0  4  4
 0  0  4  4  0  4  4  0  0  4  4  0  0  4  4  0  0  4  4  4  4  0  0  0  4  4  0  4  4  0  0  4  4  0  4  4  0  0  4  4  0  4  4  0  0  0  4  4  0  0  0  4  4  0  4  4

generates a code of length 56 over Z8 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+20x^57+3x^58+4x^59+3x^60+1x^62

The gray image is a code over GF(2) with n=224, k=5 and d=114.
This code was found by Heurico 1.16 in 0.0422 seconds.